Decision makers typically overweight small probabilities and underweight large probabilities. However, there are recent reports that when probability is presented in the form of relative frequencies, this typical pattern reverses. We tested this hypothesis by comparing decision making in two tasks: In one task, probability was stated numerically, and in the other task, it was conveyed through a visual representation. In the visual task, participants chose whether a "stochastic bullet" should be fired at either a large target for a small reward or a small target for a large reward. Participants' knowledge of probability in the visual task was the result of extensive practice firing bullets at targets. In the classical numerical task, participants chose between pairs of lotteries with probabilities and rewards matched to the probabilities and rewards in the visual task. We found that participants' probability-weighting functions were significantly different in the two tasks, but the pattern for the visual task was the typical, not the reversed, pattern.

Researchers have conjectured that eye movements during visual search are selected to minimize the number of saccades. The optimal Bayesian eye movement strategy minimizing saccades does not simply direct the eye to whichever location is judged most likely to contain the target but makes use of the entire retina as an information gathering device during each fixation. Here we show that human observers do not minimize the expected number of saccades in planning saccades in a simple visual search task composed of three tokens. In this task, the optimal eye movement strategy varied, depending on the spacing between tokens (in the first experiment) or the size of tokens (in the second experiment), and changed abruptly once the separation or size surpassed a critical value. None of our observers changed strategy as a function of separation or size. Human performance fell far short of ideal, both qualitatively and quantitatively.

Humans commonly face choices between multiple options with uncertain outcomes. Such situations occur in many contexts, from purely financial decisions (which shares should I buy?) to perceptuo-motor decisions between different actions (where should I aim my shot at goal?). Regardless of context, successful decision-making requires that the uncertainty at the heart of the decision-making problem is taken into account. Here, we ask whether humans can recover an estimate of exogenous uncertainty and then use it to make good decisions. Observers viewed a small dot that moved erratically until it disappeared behind an occluder. We varied the size of the occluder and the unpredictability of the dot's path. The observer attempted to capture the dot as it emerged from behind the occluded region by setting the location and extent of a 'catcher' along the edge of the occluder. The reward for successfully catching the dot was reduced as the size of the catcher increased. We compared human performance with that of an agent maximizing expected gain and found that observers consistently selected catcher size close to this theoretical solution. These results suggest that humans are finely tuned to exogenous uncertainty information and can exploit it to guide action.

In decision from experience, the source of probability information affects how probability is distorted in the decision task. Understanding how and why probability is distorted is a key issue in understanding the peculiar character of experience-based decision. We consider how probability information is used not just in decision-making but also in a wide variety of cognitive, perceptual, and motor tasks. Very similar patterns of distortion of probability/frequency information have been found in visual frequency estimation, frequency estimation based on memory, signal detection theory, and in the use of probability information in decision-making under risk and uncertainty. We show that distortion of probability in all cases is well captured as linear transformations of the log odds of frequency and/or probability, a model with a slope parameter, and an intercept parameter. We then consider how task and experience influence these two parameters and the resulting distortion of probability. We review how the probability distortions change in systematic ways with task and report three experiments on frequency distortion where the distortions change systematically in the same task. We found that the slope of frequency distortions decreases with the sample size, which is echoed by findings in decision from experience. We review previous models of the representation of uncertainty and find that none can account for the empirical findings.

In decision under risk, people choose between lotteries that contain a list of potential outcomes paired with their probabilities of occurrence. We previously developed a method for translating such lotteries to mathematically equivalent "motor lotteries." The probability of each outcome in a motor lottery is determined by the subject's noise in executing a movement. In this study, we used functional magnetic resonance imaging in humans to compare the neural correlates of monetary outcome and probability in classical lottery tasks in which information about probability was explicitly communicated to the subjects and in mathematically equivalent motor lottery tasks in which probability was implicit in the subjects' own motor noise. We found that activity in the medial prefrontal cortex (mPFC) and the posterior cingulate cortex quantitatively represent the subjective utility of monetary outcome in both tasks. For probability, we found that the mPFC significantly tracked the distortion of such information in both tasks. Specifically, activity in mPFC represents probability information but not the physical properties of the stimuli correlated with this information. Together, the results demonstrate that mPFC represents probability from two distinct forms of decision under risk.

Under typical viewing conditions, human observers readily distinguish between materials such as silk, marmalade, or granite, an achievement of the visual system that is poorly understood. Recognizing transparent materials is especially challenging. Previous work on the perception of transparency has focused on objects composed of flat, infinitely thin filters. In the experiments reported here, we considered thick transparent objects, such as ice cubes, which are irregular in shape and can vary in refractive index. An important part of the visual evidence signaling the presence of such objects is distortions in the perceived shape of other objects in the scene. We propose a new class of visual cues derived from the distortion field induced by thick transparent objects, and we provide experimental evidence that cues arising from the distortion field predict both the successes and the failures of human perception in judging refractive indices.

Vision provides information about the properties and identity of objects. The ease with which we perceive object properties belies the difficulty of the underlying information-processing task. In the case of object color, retinal information about object reflectance is confounded with information about the illumination as well as about the object's shape and pose. There is no obvious rule that allows transformation of the retinal image to a color representation that depends primarily on object surface reflectance. Under many circumstances, however, object color appearance is remarkably stable across scenes in which the object is viewed. Here, we review a line of experiments and theory that aim to understand how the visual system stabilizes object color appearance. Our emphasis is on models derived from explicit analysis of the computational problem of estimating the physical properties of illuminants and surfaces from the retinal image, and experiments that test these models. We argue that this approach has considerable promise for allowing generalization from simplified laboratory experiments to richer scenes that more closely approximate natural viewing. We discuss the relation between the work we review and other theoretical approaches available in the literature.

Recent studies indicate that cognitively intact individuals experience frequent rightward collisions while walking through narrow doorways. Such a directional bias has been attributed to an attentional bias in spatial perception. However, these studies did not investigate the involvement of any motor factor that could affect the directional bias in the body. In the present study, three experiments were conducted to quantify the impact of the leading foot when crossing a doorway threshold on the directional bias in the body midpoint when passing through the doorway. Participants walked through the perceived center of a relatively wide doorway. Measurements of the deviation of the upper-body midpoint from the center of the doorway demonstrated that the leading foot had a very strong influence on the directional bias. Some participants showed rightward deviation irrespective of which foot was used to step through the doorway (Experiment 1). However, a consistent rightward bias in the body was not observed in other experiments. Both the movement of one hand (Experiment 2) and covert visual attention to one side of the door (Experiment 3) caused contralateral deviation of the body. It is likely that the movement of the hand and a visual stimulus serve as an attentional cue and are effective to avoid neglect of the ipsilateral side; as a result, the body midpoint is deviated to the contralateral side. From these findings, we conclude that the directional bias in locomotor trajectories while passing through a doorway results from the combination of a motor factor, particularly the leading foot, and attentional/brain factors.

We developed a method analogous to classification images that allowed us to measure the influence that each dot in a dot cluster had on observers' estimates of the center of the cluster. In Experiment 1, we investigated whether observers employ a robust estimator when estimating the centers of dot clusters that were drawn from a single distribution. Most observers' fitted influences did not differ significantly from that predicted by a center-of-gravity (COG) estimator. Such an estimator is not robust. In Experiments 2 and 3, we considered an alternative approach to the problem of robust estimation, based on source separation, that makes use of the visual system's ability to segment visual data. The observers' task was to estimate the center of one distribution when viewing complex dot clusters that were drawn from a mixture of two distributions. We compared human performance to that of an ideal observer that separated the cluster into two sources through a maximum likelihood algorithm and based its estimates of location using the dots it assigned to just one of the two sources. The results suggest that robust methods employed by the visual system are closely tied to mechanisms of perceptual segmentation.

Statistical decision theory (SDT) and Bayesian decision theory (BDT) are closely related mathematical frameworks used to model ideal performance in a wide range of visual and motor tasks. Their elements (gain function, likelihood, prior) are readily interpretable in terms of information available to the observer. We briefly describe SDT and BDT and then review recent work employing them as models of biological perception or action. We emphasize work that employs gain functions and priors as independent or dependent variables. At one extreme, Bayesian decision theory allows the experimenter to compute ideal performance in specific tasks and compare human performance to ideal (Geisler, 1989). No claim is made that visual processing is in any sense "Bayesian". At the other extreme, researchers have proposed Bayesian decision theory as a process model of "perception as Bayesian inference"(Knill & Richards, 1996). We end by discussing how possible ideal models are related to imperfect, actual observers and how the "Bayesian hypothesis" can be tested experimentally.